2 research outputs found
On a family of binary completely transitive codes with growing covering radius
A new family of binary linear completely transitive (and, therefore,
completely regular) codes is constructed. The covering radius of these codes is
growing with the length of the code. In particular, for any integer r > 1,
there exist two codes with d=3, covering radius r and length 2r(4r-1) and
(2r+1)(4r+1), respectively. These new completely transitive codes induce, as
coset graphs, a family of distance-transitive graphs of growing diameter.Comment: Submitted to Discrete mathematics. March 10, 201
On Completely Regular Codes
This work is a survey on completely regular codes. Known properties,
relations with other combinatorial structures and constructions are stated. The
existence problem is also discussed and known results for some particular cases
are established. In particular, we present a few new results on completely
regular codes with covering radius 2 and on extended completely regular codes